You can get waterproof coax connectors, though there's a bit tough to find. They have a rubber gasket in them that seals the connection.

Another option is to use standard compression coax connectors, but put heat shrink tubing around the outside to seal them.

If you have to locate the splitter in a location where it is more directly exposed to the elements (eg, not underneath a soffit or something), you might want to get a PVC box, and then put waterproof box connectors on it, which have a gasket that seals around any kind of wire. This will provide the best waterproofing.

I've had a coax junction screwed to the outside of my house for years (probably close to a decade) -- the only protection we have is that the cables connecting to it were made w/ the 'outdoor' type ends.

If you really wanted an enclosure, you could use an electrical box with a weatherproof cover, feed the cables up from below, make the connections, then shove everything in the box and close it ... but it's going to make it harder if you ever want to change things out. (I've changed mine out a few times as I've changed between cable & satellite a few times.)

Just did this recently when I installed my new antenna tower. I picked up an outdoors electrical junction box to contain my grounding setup. I couldn't get ahold of any of the old "outdoors" style coax connectors (seem to have gone out of style), so I used the normal coax connectors, crimped on, then filled with dielectric coax sealant gel. I also had some of the weather proofing "putty" to put around the connectors, but have not done so yet as the configuration as it stands seems to be quite sound.